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# Difference between revisions of "Sudoku/Reviews/Systematic Sudoku/Nakex83"

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This puzzle came from

## Sysudoku discussion

Previously, Sysudoku presented Nakamoto Extreme 43 Redefines Sysudoku Extreme, with this comment:

This post recounts another AIC building project of 15 boomerangs, Nakamoto Extreme 43. The Nakamoto Extreme collection justifies the ‘extreme’ label by possibly exhausting the time and patience of a human solver. Let’s say, if a puzzle justifies a trial for that reason, its extreme.

Then, 63 was presented with Sudokuwiki Ends Nakex 63 On Its Own and then 83:

Nakamoto 83 earns its Extreme badge by an extremely tough Basic, and resistance to anything short of AIC building. It ends with an expanding cluster, accelerated by a series of BARNs. This post brings you to the first one, and leaves it to you to find the rest, before the March 10 post.
The line marked grid is evidence of the extremely tough basic phase, with many long line fill lists and cells of four and five candidates.

## Preliminary remarks

Sysudoku proceeds to use his patented Notation from Hell, his idiosyncratic language, and indulges in his habit of creating solution path diagrams that would confuse any genius trying to understand them. Not saying he is wrong.

He has a glossary, I think it's been improved since when I last looked at it.

• AIC is standard language, Alternating Interference Chains, a fish bicycle beloved of some.
• boomerang, boomer – an AIC loop starting with a slink and closing with a wink into a second candidate of the starting cell. If the cell has 3 or more candidates, an internal wink closes the loop and the re-entry candidate is removed. Boomers are normally spotted in the AIC building stage of Sysudoku Advanced.
• slink – strong link: a link between candidates in which at least one partner is true. A slink is represented by a solid curve in his diagrams.
• wink, weak link – a link between candidates in which both partners cannot be true. When one is proved true, the other is false. On Sysudoku grids, winks are dashed curves.

This is an example of counter-intuitive language in the Sudoku world. To me, the wink is "stronger" than the slink, it provides more information. A wink operates in both directions for inference, but a slink does not. But sysudoku did not create this mess, which simply acts as a barrier to newcomers.

A boomerang is a standard chain elimination with a loop. It's routine in Simultaneous Bivalue Nishio, and the user doesn't need to care what started the chain, nor about whether links are weak or strong, nor whether they alternate or not. If a cell is colored already in one chain, and the opposing chain eliminates a different candidate in that cell, that elimination is unconditional, because it will occur with both chains.

There is a lost performative in the Sysudoku definition of "extreme." Whose time and patience is exhausted? There is no sudoku that can do this with a knowledgeable solver willing to spend a day with a puzzle. In fact, it appears to take about four hours with "unsolvables," much more difficult than what is presented here. This puzzle did not come close to that, it was easily cracked without fuss, just several seed studies. SBN requires far less complexity to solve than what he documents.

To be sure, my documentation does not show each little obvious coloring, it only presents what is needed so that someone who knows how to color can solve the puzzle more quickly than doing it all by themselves. It is that tracing of each coloring extension that makes the Sysudoku presentations impenetrable. That would be better done with a video, or a slide deck could be better, using actual coloring.

In presenting puzzle analysis, I always like to link to SW Solver, because most anyone can access that tool. I also use Hodoku for coloring, because it is freely available and will run on about any personal computer, as a Java app. It's efficient and fast. I'm not sure what Sysudoku is using. It might be simply a drawing program. Color that slow.

## Solution with Simultaneous Bivalue Nishio

### First coloring

Some seed pairs with lower Gordonian cell number were examined and rejected. r5c5={36} looked better and some time was spent with it. A mutual resolution was found, but the coloring was then abandoned as not easily generating more results.
SBN on r5c5={36}

SBN coloring

• light orange cell: seed cell for chaining
• green: first chain. Convention: lowest digit or Gordonian cell number.
light green: alternate cell candidate within green chain.
• red: alternate chain.
light red: alternate cell candidate within red chain.
• purple: mutual elimination.
• light purple cell: contradiction (multiple in region or empty in color)
• light blue cell: mutual resolution (as only colored candidate in cell)

### Second coloring

The next seed pair was r2c3={34}. This found a contradiction in the 4 chain, hence r2c3=3, and consequences.

SBN on r2c3={34}

### Third coloring:

r5c2={75}. Contradiction found in the 5 pair, so r5c2=7. Easy to the end.

SBN on r5c2={75}